An introduction to category theory as a rigorous flexible and coherent modeling language that can be used across the sciencesCategory theory was invented in the 1940s to unify and synthesize different areas in mathematics and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics This book shows that category theory can be useful outside of mathematics as a rigorous flexible and coherent modeling language throughout the sciences Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways and the ability to translate between such organizational structures is becoming increasingly important in the sciences Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplinesWritten in an engaging and straightforward style and assuming little background in mathematics the book is rigorous but accessible to non mathematicians Using databases as an entry to category theory it begins with sets and functions then introduces the reader to notions that are fundamental in mathematics monoids groups orders and graphscategories in disguise After explaining the big three concepts of category theorycategories functors and natural transformationsthe book covers other topics including limits colimits functor categories sheaves monads and operads The book explains category theory by examples and exercises rather than focusing on theorems and proofs It includesthan 300 exercises with solutions Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation neuroscience and physics.

category pdf theory ebok sciences pdf Category Theory ebok for the download Theory for the download Category Theory for the Sciences PDFAn introduction to category theory as a rigorous flexible and coherent modeling language that can be used across the sciencesCategory theory was invented in the 1940s to unify and synthesize different areas in mathematics and it has proven remarkably successful in enabling powerful communication between disparate fields and subfields within mathematics This book shows that category theory can be useful outside of mathematics as a rigorous flexible and coherent modeling language throughout the sciences Information is inherently dynamic; the same ideas can be organized and reorganized in countless ways and the ability to translate between such organizational structures is becoming increasingly important in the sciences Category theory offers a unifying framework for information modeling that can facilitate the translation of knowledge between disciplinesWritten in an engaging and straightforward style and assuming little background in mathematics the book is rigorous but accessible to non mathematicians Using databases as an entry to category theory it begins with sets and functions then introduces the reader to notions that are fundamental in mathematics monoids groups orders and graphscategories in disguise After explaining the big three concepts of category theorycategories functors and natural transformationsthe book covers other topics including limits colimits functor categories sheaves monads and operads The book explains category theory by examples and exercises rather than focusing on theorems and proofs It includesthan 300 exercises with solutions Category Theory for the Sciences is intended to create a bridge between the vast array of mathematical concepts used by mathematicians and the models and frameworks of such scientific disciplines as computation neuroscience and physics.